18 Rational2bAdd&Subtract Unlike Denom Notes pd3.notebook 1 February 22, 2018 Mar 2912:31 PM Rational Functions 2b: Add & Subtract with Unlike Denominators Learning Targets : • How do you find the Least Common Denominator? • How do you change fractions to have the same denominator? Standards: AAPR.7, ASSE.1a GLO: #3 Complex Thinker Math Practice : #7 Look for & make use of Structure
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Rational Functions 2b: Add & Subtract with Unlike Denominators · 18 Rational2bAdd&Subtract Unlike Denom Notes pd3.notebook 6 February 22, 2018 Feb 269:48 PM Adding and Subtracting
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When adding or subtracting rational numbers such as 1/18 and 1/30 , you must first find the least common multiple (LCM) of the denominator, because rational numbers cannot be added/subtracted if they do not have the same denominator. The same is true for rational expressions.
Finding the Least Common Mulitple (LCM)1. Completely factor each monomial or polynomial. If a factor is repeated, use an exponent to indicate this.2. To determine the LCM, bring out what the denominators have in common, then bring out anything leftover.
For each polynomial, list out the factors in a row. Keep the factors aligned in columns, with a different column for each factor (whether it is a monomial or a binomial).
Factors of :
Factors of :
To determine the LCM, look in each column and select the term they have in common, add in the leftover terms, then multiply the terms together.
Adding and Subtracting Rational Expressions:1. Find the least common multiple (LCM) of the
denominators. (Also known as the least common denominator LCD)
2. For each rational expression, find an equivalent expression that has the LCM as its denominator. (Multiply the denominator by its “missing” factors. Multiply the numerator by the same factors.)
3. If necessary, simplify each numerator by multiplying terms together.
4. Add or subtract across the numerator only. The LCM will remain as the denominator.
If subtracting, be sure to distribute the negative sign to each term in the second expression’s numerator.
5. If possible, factor the numerator completely. If any factors cancel from the numerator and the denominator, simplify.
6. Find the domain restriction (excluded values): Set each factor from the LCM ≠ 0 and solve.